1. Field of the Invention
This invention relates to an area cutting method and, more particularly, to an area cutting method for cutting the interior of an area, which is bounded by a closed curve, upon dividing the area into a plurality of areas.
2. Description of the Related Art
Forms of numerically controlled machining include cutting in which the interior of an area bounded by a closed curve is hollowed out down to a predetermined depth, and die milling in which the interior of an area is die milled. In such machining, as shown in FIG. 10(A), an area cutting method is conventionally carried out by performing cutting along an (i-1)th cutting path PTi-1 in one direction (the direction of the solid line arrow), raising the tool a predetermined amount at the completion of cutting, then positioning the tool directly above a cutting starting point Ps on the next, or i-th, cutting path PTi, thereafter lowering the tool to the cutting starting point Ps, moving the tool along the i-th cutting path PTi in the direction of the solid line arrow, and subsequently repeating the above unidirectional cutting.
Another area cutting method shown in FIG. 10(B) includes, following completion of cutting along the cutting path PTi-1 of the (i-1)th cutting path, moving the tool from a cutting end point Pe to the cutting starting point Ps on the next, or i-th, cutting path, and thereafter performing cutting along the i-th cutting path PTi. Thus, cutting is performed back and forth in the direction of the arrows.
Still another area cutting method shown in FIG. 10(C) includes obtaining offset paths OFC1, OFC2, . . . OFCn offset by predetermined amounts with respect to a curve OLC of an external shape, and moving the tool successively along the offset paths.
However, with the first area cutting method based on unidirectional cutting, the tool must be positioned at the cutting starting point Ps on the i-th cutting path PTi after the completion of cutting along the (i-1)th cutting path PTi-1. This method is disadvantageous in that it results in a long tool traveling distance.
With the second cutting method based on reciprocative cutting, portions are left uncut. In order to cut the uncut portions, the tool must be moved along the external shape curve OLC at completion of the back-and-forth cutting, thereby necessitating both back-and-forth cutting control and cutting control along the shape of the external curve. Accordingly, this method is disadvantageous in that control is complicated. Further, if an area AR has concavities and convexities, as shown in FIG. 10(D), the second method requires movement for achieving positioning indicated by the dashed lines. This is disadvantageous in that tool travelling distance and cutting time are prolonged. In addition, since the cutting process for the outward trip is different from the cutting process for the return trip, cutting cannot be performed efficiently overall. It should be noted that the cutting processes referred to here indicate up cutting and down cutting processes. FIGS. 11(A) and 11(B) show examples of the down cutting process, and FIGS. 11(C), (D) depict examples of the up cutting process. If the workpiece material has been decided, then a cutting method capable of cutting the workpiece efficiently is selected from the up cutting and down cutting processes. However, with the second method, the up cutting process [e.g. FIG. 11(A)] and the down cutting process [e.g. FIG. 11(C)] are always mixed, so that cutting cannot be performed efficiently.
With the third method of cutting along the offset paths, portions are left uncut at, e.g., the central portion of the area, depending upon the contour of the external shape curve. This method is disadvantageous in that dealing with these uncut portions is a complicated task.
Accordingly, in order to eliminate the aforementioned drawbacks of the conventional method, the applicant has proposed a method in which a tool path in the form of a spider web pattern is decided within the area and a tool is moved along the tool path to machine area. For example, refer to the U.S. Pat. No. 4,706,201) FIGS. 12(A), (B) are views for describing this area cutting method.
The area cutting method is as follows:
(a) It is determined whether there is a need to divide an area AR bounded by a closed curve OLC. PA1 (b) If division is not necessary [see FIG. 12(A)], line segments L1-L7 connecting the centroid W and apices Pi (i=1, 2, . . . 7) are partitioned at a predetermined number of partitions. PA1 (c) Closed curves CPTi successively connecting the corresponding partitioning points Pi1.fwdarw.Pi2.fwdarw.Pi3.fwdarw.Pi5.fwdarw.Pi6 (i=1, 2, . . . 4) of the line segments are generated, and area cutting is performed by moving a tool along the generated closed paths. PA1 (d) If division is necessary [see FIG. 12(B)], the area AR is divided into a plurality of areas PG1, PG2. PA1 (e) Centroids W1, W2 of these divided areas are calculated and a number of partitions which will provide the largest cut-in pitch without exceeding an allowable value is obtained for each divided area. PA1 (f) Line segments L11-L15, L21-L24 of the divided areas PG1, PG2 are partitioned at the respective number of partitions. PA1 (g) Closed paths CPAi, CPBj connecting the corresponding partitioning points Qi1.fwdarw.Qi2.fwdarw.. . . Qi5 (i=1, 2, . . . ), Rj1.fwdarw.Rj2.fwdarw.. . . Rj4 (j=1, 2, . . . ) of the line segments are obtained for the respective divided areas PG1, PG2, and area cutting is performed by moving the tool along each closed path. PA1 (1) The centroid W of the area is obtained. PA1 (2) A check is performed as to whether a line segment connecting the centroid and an i-th (the initial value of i is 1) apex Pi intersects the closed curve OLC. PA1 (3) If the line segment does not intersect the closed curve, the operation i+1.fwdarw. i is performed and the discrimination processing of step (2) is executed. PA1 (4) If the line segment does intersect the closed curve, a polygon P1P2 . . . Pi-1 is made the first divided area PG1. PA1 (5) If the processing of steps (1)-(4) is subsequently repeated for the polygons PiPi+1 . . . P1, the area AR will be divided into a plurality of areas. In the example of FIG. 12(B), the area is divided into two areas, namely polygon P1P2P3P4P5 and polygon P5P6P7P1.
The area dividing method is as follows:
However, in accordance with this process for dividing an area in the cutting of an area in a spider web-like pattern, the area is merely divided in such a manner that the line segments connecting the centroid Wi and apices Pi of the divided areas do not intersect the closed curve OLC. Consequently, there are cases where a divided area takes on an elongated, slender shape [see divided area PG2 in FIG. 12(B)]. Tool paths are generated by (a) obtaining the length l of the longest line segment among the line segments connecting the centroid and apices of each divided area, (b) obtaining the largest integer that satisfies the relation EQU P.gtoreq.l/n
using l and a predetermined cut-in pitch P, (c) adopting the integer n as the number of partitions and dividing each line segment into n equal parts, and (d) obtaining, for each divided area, a plurality of tool paths successively connecting the partitioning points of the line segments, and combining these tool paths.
As a result, when an area takes on the elongated, slender shape, a high tool path density occurs at the narrow portions of the area, as is clearly shown in FIG. 12(B). This represents an increase wasted tool movement and diminishes cutting efficiency.
Accordingly, an object of the present invention is to provide an area cutting method through which the occurrence of elongated, slender areas can be minimized when dividing an area.
Another object of the present invention is to provide an area cutting method through which wasted tool movement can be reduced to improve cutting efficiency.